Orthogonality and Least Squares Method

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Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Orthogonality, Triangle Inequality, Pythagorean Theorem

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

Orthogonality: Norm, Scalar Product, Perpendicularity

Covers norm, scalar product, and perpendicularity in R^n, including the theorem of Pythagoras and orthogonal complements.

Orthogonality and Subspaces

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Signals & Systems I: Vector Approximation and Signal Comparison

Explores vector approximation, signal detection, correlation, Fourier series, and signal comparison in signals and systems.

Orthonormal Vectors Properties

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Real Vector Space: Basics

Introduces the basics of real vector spaces, norms, and scalar products.